Considering spatial and temporal scale in landscape-genetic studies of gene flow.

Landscape features exist at multiple spatial and temporal scales, and these naturally affect spatial genetic structure and our ability to make inferences about gene flow. This article discusses how decisions about sampling of genotypes (including choices about analytical methods and genetic markers) should be driven by the scale of spatial genetic structure, the time frame that landscape features have existed in their current state, and all aspects of a species' life history. Researchers should use caution when making inferences about gene flow, especially when the spatial extent of the study area is limited. The scale of sampling of the landscape introduces different features that may affect gene flow. Sampling grain should be smaller than the average home-range size or dispersal distance of the study organism and, for raster data, existing research suggests that simplifying the thematic resolution into discrete classes may result in low power to detect effects on gene flow. Therefore, the methods used to characterize the landscape between sampling sites may be a primary determinant for the spatial scale at which analytical results are applicable, and the use of only one sampling scale for a particular statistical method may lead researchers to overlook important factors affecting gene flow. The particular analytical technique used to correlate landscape data and genetic data may also influence results; common landscape-genetic methods may not be suitable for all study systems, particularly when the rate of landscape change is faster than can be resolved by common molecular markers.

Perspectives on the use of landscape genetics to detect genetic adaptive variation in the field.

Understanding the genetic basis of species adaptation in the context of global change poses one of the greatest challenges of this century. Although we have begun to understand the molecular basis of adaptation in those species for which whole genome sequences are available, the molecular basis of adaptation is still poorly understood for most non-model species. In this paper, we outline major challenges and future research directions for correlating environmental factors with molecular markers to identify adaptive genetic variation, and point to research gaps in the application of landscape genetics to real-world problems arising from global change, such as the ability of organisms to adapt over rapid time scales. High throughput sequencing generates vast quantities of molecular data to address the challenge of studying adaptive genetic variation in non-model species. Here, we suggest that improvements in the sampling design should consider spatial dependence among sampled individuals. Then, we describe available statistical approaches for integrating spatial dependence into landscape analyses of adaptive genetic variation.

Utility of computer simulations in landscape genetics.

Population genetics theory is primarily based on mathematical models in which spatial complexity and temporal variability are largely ignored. In contrast, the field of landscape genetics expressly focuses on how population genetic processes are affected by complex spatial and temporal environmental heterogeneity. It is spatially explicit and relates patterns to processes by combining complex and realistic life histories, behaviours, landscape features and genetic data. Central to landscape genetics is the connection of spatial patterns of genetic variation to the usually highly stochastic space-time processes that create them over both historical and contemporary time periods. The field should benefit from a shift to computer simulation approaches, which enable incorporation of demographic and environmental stochasticity. A key role of simulations is to show how demographic processes such as dispersal or reproduction interact with landscape features to affect probability of site occupancy, population size, and gene flow, which in turn determine spatial genetic structure. Simulations could also be used to compare various statistical methods and determine which have correct type I error or the highest statistical power to correctly identify spatio-temporal and environmental effects. Simulations may also help in evaluating how specific spatial metrics may be used to project future genetic trends. This article summarizes some of the fundamental aspects of spatial-temporal population genetic processes. It discusses the potential use of simulations to determine how various spatial metrics can be rigorously employed to identify features of interest, including contrasting locus-specific spatial patterns due to micro-scale environmental selection.

Spatial correlations at different spatial scales are themselves highly correlated in isolation by distance processes.

Although many properties of spatial autocorrelation statistics are well characterized, virtually nothing is known about possible correlations among values at different spatial scales, which ultimately would influence how inferences about spatial genetics are made at multiple spatial scales. This article reports the results of stochastic space-time simulations of isolation by distance processes, having a very wide range of amounts of dispersal for plants or animals, and analyses of the correlations among Moran's I-statistics for different mutually exclusive distance classes. In general, the stochastic correlations are extremely large (>0.90); however, the correlations bear a complex relationship with level of dispersal, spatial scale and spatial lag between distance classes. The correlations are so large that any existing or conceived statistical method that employs more than one distance class (or spatial scale) should not ignore them. This result also suggests that gains in statistical power via increasing sample size are limited, and that increasing numbers of assayed loci generally should be preferred. To the extent that sampling error for real data sets can be treated as white noise, it should be possible to account for stochastic correlations in formulating more precise statistical methods. Further, while the current results are for isolation by distance processes, they provide some guidance for some more complex stochastic space-time processes of landscape genetics. Moreover, the results hold for several popular measures other than Moran's I. In addition, in the results, the signal to noise ratios strongly decreased with distance, which also has several implications for optimal statistical methods using correlations at multiple spatial scales.

Chloroplast diversity in a putative hybrid swarm of Ponderosae (Pinaceae).

The Ponderosae subsection of the genus Pinus contains numerous taxa in disjunct mountain ranges of southern Arizona and New Mexico, differing for several leaf and cone traits, key among which is the number of leaf needles per fascicle. Trees with three needles are often found together with trees having five needles and mixed numbers. One taxonomic hypothesis is that there are swarms of hybrids between P. ponderosa and P. arizonica. A second hypothesis is that there are spatial mixtures of two separate taxa, five-needle P. arizonica and a "taxon X" containing three needle and mixed needle trees. We genotyped chloroplasts in one putative hybrid swarm on Mt. Lemmon using microsatellite markers and show that cpDNA is almost completely differentiated between two separate morphotypes corresponding to P. arizonica and "taxon X." Little if any introgression has occurred on Mt. Lemmon, and the simplest explanation is that little or no effective hybridization has occurred. Further results indicate that not only is taxon X not of hybrid origin, it is more closely related to nonregional Ponderosae other than P. ponderosa and P. arizonica. The results further suggest that other putative hybrid swarms in the region are also spatial mixtures of distinct taxa.

Plant dispersal, neighbourhood size and isolation by distance.

A theoretical relationship between isolation by distance or spatial genetic structure (SGS) and seed and pollen dispersal is tested using extensive spatial-temporal simulations. Although for animals Wright's neighbourhood size N(e) = 4pisigma(2)(t) has been ascertained also, where sigma(2)(t) is the axial variance of distances between parents and offspring, and it was recently confirmed that N(e) = 4pi(sigma(2)(f) + sigma(2)(m))/2 when dispersal of females and males differ, the situation for plants had not been established. This article shows that for a very wide range of conditions, neighbourhood size defined by Crawford's formula N(e) = 4pi(sigma(2)(s) + sigma(2)(p)/2) fully determines SGS, even when dispersal variances of seed (sigma(2)(s)) and pollen sigma(2)(p)) differ strongly. Further, self-fertilization with rate s acts as zero-distance pollen dispersal, and N(e) = 4pi[sigma(2)(s) + sigma(2)(p)(1 - s)/2] fully determines SGS, for most cases where there are both likely parameter values and substantial SGS. Moreover, for most cases, there is a loglinear relationship, I(1) = 0.587 - 0.117 ln(N(e)), between SGS, as measured by I(1), Moran's coefficient for adjacent individuals, and N(e). However, there are several biologically significant exceptions, namely for very low or large N(e), SGS exceeds the loglinear values. There are also important exceptions to Crawford's formula. First, plants with low seed dispersal, high outcross pollen dispersal and high selfing rate show larger SGS than predicted. Second, in plants with very low (near zero) seed dispersal, selfing decreases SGS, opposite expectations. Finally, in some cases seed dispersal is more critical than pollen dispersal, in a manner inconsistent with Crawford's formula.

Mutation at high rates reduces spatial structure within populations.

The question of whether or not the high rates (mu) of mutation that occur for some hypervariable markers can affect commonly used empirical measures of spatial structure of genetic variation within populations is addressed. The results show that values of these measures are approximately halved when mu is 10(-2). Finest spatial-scale correlations, measured by either Moran's I-statistics or conditional kinship, are reduced by 30%-50%. When the mutation rate is 10 times lower, much smaller reductions result, e.g. averaging 7% for the finest scale correlations. Still smaller orders of magnitude of mu cause negligible changes in spatial structure, where any effects normally would not be detectable. The reductions are caused by forward mutations, and when the reductions are measured as percentages, they are nearly independent of the amount of structure produced sans mutation, except when dispersal is nearly minimal. The percent reductions are also nearly independent of the number of alleles and of back mutations, hence of the nature of the mutation process (e.g. stepwise or not). The results demonstrate that some hypervariable loci should have reduced spatial structuring, and that marker choice may affect the values observed in experimental surveys. Moreover, if fine-scale correlations are used to indirectly estimate dispersal distances, then mutation at high rates could inflate estimates, easily up to two- to three-fold.

Geographic pattern of genetic diversity in Pinus resinosa: contact zone between descendants of glacial refugia.

Although red pine (Pinus resinosa) generally has low or completely lacks variation for molecular markers, some variation is observed for chloroplast microsatellites (cpSSRs). We sampled and examined 10 cpSSRs for 19 populations. Analysis of these populations plus 10 previously studied populations shows that the geographic distribution of genetic diversity over the range of P. resinosa is markedly nonuniform. Although the pattern exhibits little isolation by distance, there is a region centered in northeastern New England where populations contain much greater chloroplast haplotype diversity than elsewhere. This area is band-shaped, with the longer axis nearly parallel with latitude, and very sharply delineated. The area of high diversity was buried by the Laurentide ice sheet. The geographic pattern indicates that P. resinosa is not at equilibrium, and the species has had a more complex postglacial history than typically purported for forest trees in eastern North America. The results suggest that the area of high diversity is a stable transition zone between descendants of two distinct refugia, one in the southern Appalachians and another near the North Atlantic coastline of the Wisconsinian glacial period. Plausible explanations are given that selection between two lineages, along latitudinal zones, may have maintained the transition zone.

Spatial and population genetic structure of microsatellites in white pine.

We evaluated the population genetic structure of seven microsatellite loci for old growth and second growth populations of eastern white pine (Pinus strobus). From each population, located within Hartwick Pines State Park, Grayling, Michigan, USA, 120-122 contiguous trees were sampled for genetic analysis. Within each population, genetic diversity was high and inbreeding low. When comparing these populations, there is a significant, but small (less than 1%), genetic divergence between populations. Spatial distance between populations or timber harvest at the second growth site were reasonable explanations for the observed minor differences in allele frequencies between populations. Spatial autocorrelation analysis suggested that, for the old growth population, weak positive structuring at 15 m fits the isolation by distance model for a neighbourhood size of about 100 individuals. In comparison, genotypes were randomly distributed in the second growth population. Thus, logging may have decreased spatial structuring at the second growth site, suggesting that management practices may be used to alter natural spatial patterns. In addition, the amount of autocorrelation in the old growth population appears to be lower for some of the microsatellites, suggesting higher numbers of rare alleles and that higher mutation rates may have directly affected spatial statistics by reducing structure.

Microsatellite analysis of spatial structure among seedlings in populations of Pinus strobus (pinaceae).

In a detailed analysis of how limited seed dispersal can create spatial structuring of genetic variation, several nuclear microsatellites were assayed in seedlings from two forests of Pinus strobus, one old growth (OG) and the other (second site, SS) logged in ca. 1900. By using loci with a large number of alleles and new statistical methods on averaged spatial correlation coefficients, unusually precise estimates of spatial genetic structure were obtained, even though the structure was expected to be very weak. This high precision allowed the spatial patterns to be contrasted across loci and populations. At the OG site, the average spatial correlation coefficient for short distances (<15 m) exceeded its random expected value by 0.035, providing an indirect estimate of ca. 230 for Wright's neighborhood size. The value is similar to that estimated in a previous study of adult trees at OG and probably represents the natural level of spatial structure. A very similar value, 0.030, was obtained for seedlings at SS, despite the fact that unlike OG, genotypes of adults are randomly distributed, a likely result of logging. The results show that a single cycle of limited seed dispersal recreated the natural level of spatial structuring. In addition, one microsatellite, Rps50, had far greater amounts of allele variation, likely implicating it as having a higher mutation rate. The spatial structure of Rps50 also was significantly reduced, in a way that could be consistent with theoretical effects of high mutation rates (up to µ = 10(-2)). The choice of markers may influence estimates of spatial genetic structure. For example, if Rps50 is omitted the values are nearly doubled to 0.058 and 0.051 for SS and OG, respectively, both indicating a much smaller neighborhood size of ca. 100.

Covariances among join-count spatial autocorrelation measures.

Spatial distributions of biological variables are often well-characterized with pairwise measures of spatial autocorrelation. In this article, the probability theory for products and covariances of join-count spatial autocorrelation measures are developed for spatial distributions of multiple nominal (e.g. species or genotypes) types. This more fully describes the joint distributions of pairwise measures in spatial distributions of multiple (i.e. more than two) types. An example is given on how the covariances can be used for finding standard errors of weighted averages of join-counts in spatial autocorrelation analysis of more than two types, as is typical for genetic data for multiallelic loci.

Genetic structure of age classes in Camellia japonica (Theaceae).

Camellia japonica L. (Theaceae), an insect- and bird-pollinated, broad-leaved evergreen tree, is widely distributed in Japan and the southern Korean peninsula. The species has a relatively even age distribution within populations, which may influence the spatial genetic structure of different age classes relative to species with typical L-shaped age distributions. To determine whether the internal spatial genetic structure found in seedlings and young individuals carries over into adults, we used allozyme loci, F-statistics, spatial autocorrelation statistics (Moran's I), and coancestry measures to examine changes in genetic structure among seven age classes in a population (60-m x 100-m area) in southern Korea. In seedlings, weak but significant positive values of Moran's I-statistics and coancestry measures were found for distances less than 14 m, which is consistent with a mechanism of limited seed dispersal combined with overlapping seed shadows. This spatial structure, however, dissipates in older age classes, and in adults genetic variation has an essentially random spatial distribution. Morisita's index of dispersion of individuals in each age class showed that seedlings and juveniles are more highly clustered than are older individuals. These results suggest that self-thinning changes the spatial relationships of individuals, and thus genotypes. A multilocus estimate of FST (0.008) shows a small but statistically significant difference in allele frequencies among age classes. In summary, intrapopulation genetic structure within and among age classes of C. japonica was significant but weak. Despite presumably limited seed dispersal, weak spatial genetic structure in juveniles suggests overlapping seed shadows followed by self-thinning during recruitment. The present study also demonstrates that studies of spatial genetic structure focusing on limited numbers of generations may not be sufficient to reveal the entire picture of genetic structure in populations with overlapping generations.

Spatial pattern of allozyme variation in a contact zone of Pinus Ponderosa and P. arizonica (Pinaceae).

The spatial distribution of genotypes for nine polymorphic allozyme loci was examined in a contact zone between Pinus ponderosa var. scopulorum and another tree regarded as either a separate species, Pinus arizonica, or variety, Pinus ponderosa var. arizonica, in southern Arizona. Previous work had identified a steep elevational cline for a key taxonomic trait, number of leaf-needles per fascicle, on the south slope of Mt. Lemmon. The present results indicate that the taxa are not fully interbreeding in this contact zone, because allozyme genotypes are considerably more spatially structured than expected for the dispersal characteristics of pines. The amount of spatial differentiation is also much less than that observed for needle number. It appears that this is due to the lack of differentiation for allozyme gene frequencies for the two types of trees, which is further evidenced by analysis of samples from two other populations away from the contact zone. It is likely that if the two taxa were isolated in the past, it was not for long enough nor complete enough to allow mutation-drift to create substantial differentiation between them. Another possible explanation is that introgression after recontact is so advanced that any differences have been erased throughout the Santa Catalina mountain range.

SPATIAL GENETIC STRUCTURE OF CLONAL AND SEXUAL REPRODUCTION IN POPULATIONS OF ADENOPHORA GRANDIFLORA (CAMPANULACEAE).

The spatial distribution of clonal versus sexual reproduction in plant populations should generally have differing effects on the levels of biparental inbreeding and the apparent selfing rate, produced via mating by proximity through limited pollen dispersal. We used allozyme loci, join-count statistics, and Moran's spatial autocorrelation statistics to separate the spatial genetic structure caused by clonal reproduction from that maintained in sexually reproduced individuals in two populations of Adenophora grandiflora, a perennial herb. Join-count statistics showed that there were statistically significant clustering of clonal genotypes within distances less than 4 m. Both the entire populations and the sets of sexually reproduced individuals exhibited significant spatial autocorrelation at less than about 12 m, and the sexually reproduced individuals are substantially structured in an isolation-by-distance manner, consistent with a neighborhood size of about 50.

GENE DISPERSAL AND SPATIAL GENETIC STRUCTURE.

Spatial autocorrelation statistics have been studied in theoretical population genetic models and widely used in experimental studies of spatial structure in many plant and animal populations. However, the statistical properties of spatial autocorrelation statistics have remained uncharacterized. Little is known about how values of spatial autocorrelation statistics in population samples depend on the level of dispersal and scheme of sampling. In this paper, we characterize the statistical properties of join-count spatial autocorrelation statistics for population genetic surveys under various conditions of dispersal and sampling. The results indicate generally high statistical power. These results can provide a method to estimate gene dispersal based on standing spatial patterns of genetic variation observed within populations.

FREQUENCY-DEPENDENT VARIATION FOR OUTCROSSING RATE AMONG FLOWER-COLOR MORPHS OF IPOMOEA PURPUREA.

In a series of previous studies, it has been shown that populations of the common morning glory Ipomoea purpurea are typically polymorphic for flower-color genes that bias pollinator service and, hence, the rate of outcrossing. In this study, we show that the rate of outcrossing for the white flower-color morph depends on its frequency in experimental populations of the morning glory. White flowers are visited less often by the primary pollinator, bumblebees, and have lower outcrossing rates than colored flowers when they are in the minority. In contrast, blue or pink flower morphs are not undervisited and do not have lowered outcrossing rates when they are rare. In plant populations where genes that increase selling are selectively favored due to their transmission bias, undervisitation of rare morphs may act to stabilize genetic variation for outcrossing rates.